John Greenlees: The torsion Adams spectral sequence for rational torus-equivariant spectra

19th October, 2021
Watch Later Cinema Mode

We provide a calculational method for rational stable equivariant homotopy theory for a torus G based on the homology of the Borel construction on fixed points. More precisely we define an abelian torsion model, π’œt(G) of finite injective dimension, a homology theory Ο€βˆ—π’œt taking values in π’œt(G) based on the homology of the Borel construction, and a finite Adams spectral sequence

Extπ’œt(G)βˆ— , βˆ— (Ο€βˆ—π’œt(X), Ο€βˆ—π’œt(Y)) β†’ [X,Y]βˆ—G

for rational G-spectra X and Y.

This approach should be viewed as an analogue of the Cousin complex in algebraic geometry. It is expected that a similar method will apply to other tensor triangulated categories with finite-dimensional Noetherian Balmer spectra.

This talk relates to this arXiv paper.

This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.